Slope from a graph and table

Front

What is the definition of slope?

Back

Slope is a measure of the steepness of a line, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you calculate the slope from a graph?

Back

To calculate the slope from a graph, select two points on the line, determine the rise (change in y) and run (change in x), and use the formula: Slope = rise/run.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the run (change in x) is 0, leading to division by zero.

Front

If a line rises from left to right, what is the sign of its slope?

Back

The slope is positive.

Front

If a line falls from left to right, what is the sign of its slope?

Back

The slope is negative.

Front

What does a slope of 1 mean in a real-world context?

Back

A slope of 1 means that for every unit increase in the x-direction, there is a corresponding unit increase in the y-direction.

Front

What does a slope of -2 represent?

Back

A slope of -2 means that for every 1 unit increase in the x-direction, there is a 2 unit decrease in the y-direction.

Front

How can you determine the slope from a table of values?

Back

To determine the slope from a table, select two points (x1, y1) and (x2, y2) and use the formula: Slope = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line represented by the points (2, 3) and (4, 9)?

Back

Slope = (9 - 3) / (4 - 2) = 6 / 2 = 3.